Ergodicity for Langevin Dynamics with Singular Potentials

par Masha Gordina (University of Connecticut)

vendredi 10 nov. 2023, 14:00 → 16:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Probability and analysis informal seminar

We discuss Langevin dynamics of N particles on R^d interacting through a singular repulsive potential, such as the Lennard-Jones potential, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance.  The proof relies on an explicit construction of a Lyapunov function using a modified Gamma calculus (Bakry-Emery).  In contrast to previous results for such systems, our results imply geometric convergence to equilibrium starting from an essentially optimal family of initial distributions. This is based on joint work with F.Baudoin and D.Herzog.

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